For certain types of rooms and some aesthetic tastes, exposed concrete flooring is a nice option. You can get concrete with a pigment color integrated into the material, you can paint the concrete, or you can simply use a clear (non-toxic) sealer for a more modern or industrial look
Many people find bamboo flooring very attractive. It looks similar to regular wood flooring, but it is harder and more durable. Bamboo has a short growing time, so it is a rapidly renewable resource. Most bamboo flooring contains trace amounts of formaldehyde; one brand that does not is Bamboo Hardwoods, and Teragren contains very low levels.